A body is suspended on a spring balance in a ship weighs wo when the ship is at rest. When the ship begind to move along the equator with a speed v , show that the scale reading is very close to wo ( 1 +_ 2wv/g ) , where w is the angular speed of the earth
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A body suspended on a spring balance in a ship weighs
′
W
0
′
when the ship is at rest. When the ship begins to move along the equator with a speed
′
v
′
, the scale reading is very close to W
0
(1±2ωv/g), where
′
ω
′
is the angular speed of the earth.
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Solution
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Verified by Toppr
When at rest, W
o
=mg−mω
2
R≈mg, as g>>ω
2
R where ω=7.3×10
−5
radians/second is angular speed of earth about its axis, and R=6.4×10
6
m is radius of earth.
now when ship moves with speed v, the effective angular speed of body is ω±
R
v
,
so new weight is
W=m(g−(ω±
R
v
)
2
R)=mg−mω
2
R+mv
2
/R±2ωv=mg±2mωv, (∵g>>ω
2
R,v
2
/R≈0)
⇒W=mg(1±2ωv/g)=W
o
(1±2ωv/g)